MathDB

Projections of points and lines

Source: Baltic Way 2007

November 30, 2010

geometry proposedgeometry

Problem Statement

Let

t_1,t_2,\ldots,t_k

be different straight lines in space, where

k>1

. Prove that points

P_i

on

t_i

,

i=1,\ldots,k

, exist such that

i=1,\ldots,k-1

is the projection of

P_i

on

t_{i+1}

for

i=1,\ldots,k-1

, and

P_1

is the projection of

P_k

on

t_1

.

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